Gauge-model With Ising Vacancies - Multicritical Behavior of Self-avoiding Surfaces

A Z2 gauge model with n-component-vector degrees of freedom on a dodecahedral lattice is coupled to an Ising system on the dual lattice. The statistics of interacting self-avoiding surfaces (SAS) is obtained in the n --> 0 limit. At the percolative critical point an exact identification of the SAS critical behavior with that of Ising cluster hulls holds. This condition corresponds to a multicritical point for SAS, in a universality class different from that of branched polymers. The model allows application of standard statistical methods to SAS. A mean-field calculation gives a phase diagram remarkably consistent with the above results.